For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?

Answer 1

let's rephrase the question.

For what values of k will the quadratic
x^2 - kx + k^2 = 0 have 2 solutions

when b^2 - 4ac > 0

k^2 - 4(1)(k^2) >0
-3k^2 > 0
k^2 < 0

any number squared is always positive, so there is no value of k for which the graph will cross the x-axis twice

you can test this here
http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2+-+5x+%2B+25

in my example I let k = 5
you can change the equation by editing the value of k, and the graph will always be above the x-axis